Mia Farrow was 22 years old when LIFE magazine ran a seven-page cover story on the actress in May 1967. She was married to Frank Sinatra (he was 30 years her senior, and the marriage lasted less than two years) and at the time was best-known for her work on TV: she was a regular on the classic prime-time soap opera, Peyton Place. But LIFE’s decision to feature the young Los Angeles native proved prescient; within a year she was receiving raves for performances in several prominent films — including the Roman Polanski horror classic, Rosemary’s Baby — and would go on to a decades-long career as an award-winning actress and an outspoken, fearless campaigner for human rights.

[Most recently, of course, Ms. Farrow has been in the headlines primarily due to renewed accusations by her adopted daughter, Dylan, that Woody Allen sexually abused her when she was a child, at a time when Allen and Ms. Farrow were in a long-term relationship. Woody Allen has always denied the charges; Ms. Farrow has never wavered in her support of Dylan’s claims.]

As portrayed in that long-ago cover story, meanwhile, at a time when one of the keenest annoyances in her life was that people sometimes confused her with Twiggy, Mia Farrow seemed to have it all — youth, beauty, talent and not a little mystery. As LIFE wrote:

There are these positive statements you can make about Mia Farrow: she is 22; she weighs 99 pounds; she is 5 feet 5 1/2 inches tall; she has less hair than Ringo Starr; she is annoyed that people in London mistake her for Twiggy; she is married to Frank Sinatra.

Beyond such unarguable specifics lies her shapeless world — a place of surmise so fascinatingly complex and maddeningly naive that Sinatra could fathom it only by marrying into it. And ever since the surprising match was made the public has been stuck on the nagging question, “What is Mia Farrow really like?”

The feature goes on to paint a picture of a whip-smart, self-deprecatingly funny daughter of Hollywood (her mother was the famous actress Maureen O’Sullivan, her dad was Oscar-winning writer and director John Farrow) — a woman barely out of her teens yet worldly enough to say of her superstar husband, Sinatra: “He’s an artist. He’s groovy, he’s kinky and — above all — he’s gentle.”

Here, on Ms. Farrow’s 69th birthday (she was born Maria de Lourdes Villiers Farrow on February 9, 1945), LIFE.com features a series of photographs — most of them unpublished — that feel, in more ways than we can count, as if they were made not only in another time, but in another world.